%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : CAT001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:07:38 PM UTC 2026
% Result : Unsatisfiable 0.21s 10.97s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/10.44 % Computer : n019.cluster.edu
% 0.17/10.44 % Model : x86_64 x86_64
% 0.17/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.44 % Memory : 8046.5625MB
% 0.17/10.44 % OS : Linux 6.8.0-71-generic
% 0.17/10.44 % CPULimit : 300
% 0.17/10.44 % WCLimit : 300
% 0.17/10.44 % DateTime : Mon Sep 21 13:55:15 UTC 2026
% 0.17/10.44 % CPUTime :
% 0.17/10.45 % Drodi V4.1.1
% 0.21/10.97 % Refutation found
% 0.21/10.97 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.21/10.97 % SZS output start CNFRefutation for theBenchmark
% 0.21/10.97 fof(f1,axiom,(
% 0.21/10.97 (![X,Y]: (( ~ defined(X,Y)| product(X,Y,compose(X,Y)) ) ))),
% 0.21/10.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/10.97 fof(f2,axiom,(
% 0.21/10.97 (![X,Y,Z]: (( ~ product(X,Y,Z)| defined(X,Y) ) ))),
% 0.21/10.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/10.97 fof(f4,axiom,(
% 0.21/10.97 (![X,Y,Xy,Z,Yz]: (( ~ product(X,Y,Xy)| ~ product(Y,Z,Yz)| ~ defined(Xy,Z)| defined(X,Yz) ) ))),
% 0.21/10.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/10.97 fof(f5,axiom,(
% 0.21/10.97 (![X,Y,Xy,Z,Xyz,Yz]: (( ~ product(X,Y,Xy)| ~ product(Xy,Z,Xyz)| ~ product(Y,Z,Yz)| product(X,Yz,Xyz) ) ))),
% 0.21/10.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/10.97 fof(f6,axiom,(
% 0.21/10.97 (![Y,Z,Yz,X]: (( ~ product(Y,Z,Yz)| ~ defined(X,Yz)| defined(X,Y) ) ))),
% 0.21/10.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/10.97 fof(f7,axiom,(
% 0.21/10.97 (![Y,Z,Yz,X,Xy]: (( ~ product(Y,Z,Yz)| ~ product(X,Y,Xy)| ~ defined(X,Yz)| defined(Xy,Z) ) ))),
% 0.21/10.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/10.97 fof(f9,axiom,(
% 0.21/10.97 (![X,Y,Z]: (( ~ defined(X,Y)| ~ defined(Y,Z)| ~ identity_map(Y)| defined(X,Z) ) ))),
% 0.21/10.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/10.97 fof(f11,axiom,(
% 0.21/10.97 (![X]: (identity_map(codomain(X)) ))),
% 0.21/10.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/10.97 fof(f15,axiom,(
% 0.21/10.97 (![X]: (product(codomain(X),X,X) ))),
% 0.21/10.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/10.97 fof(f18,axiom,(
% 0.21/10.97 (![X,Y,Z,W]: (( ~ product(X,Y,Z)| ~ product(X,Y,W)| Z = W ) ))),
% 0.21/10.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/10.97 fof(f19,hypothesis,(
% 0.21/10.97 product(a,b,c) ),
% 0.21/10.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/10.97 fof(f20,hypothesis,(
% 0.21/10.97 (![X1,X2,X3]: (( ~ product(c,X1,X2)| ~ product(c,X3,X2)| X1 = X3 ) ))),
% 0.21/10.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/10.97 fof(f21,hypothesis,(
% 0.21/10.97 product(b,h,d) ),
% 0.21/10.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/10.97 fof(f22,hypothesis,(
% 0.21/10.97 product(b,g,d) ),
% 0.21/10.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/10.97 fof(f23,negated_conjecture,(
% 0.21/10.97 h != g ),
% 0.21/10.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/10.97 fof(f24,plain,(
% 0.21/10.97 ![X0,X1]: (~defined(X0,X1)|product(X0,X1,compose(X0,X1)))),
% 0.21/10.97 inference(cnf_transformation,[status(thm)],[f1])).
% 0.21/10.97 fof(f25,plain,(
% 0.21/10.97 ![X,Y]: ((![Z]: ~product(X,Y,Z))|defined(X,Y))),
% 0.21/10.97 inference(miniscoping,[status(thm)],[f2])).
% 0.21/10.97 fof(f26,plain,(
% 0.21/10.97 ![X0,X1,X2]: (~product(X0,X1,X2)|defined(X0,X1))),
% 0.21/10.97 inference(cnf_transformation,[status(thm)],[f25])).
% 0.21/10.97 fof(f29,plain,(
% 0.21/10.97 ![X,Yz]: ((![Xy,Z]: ((![Y]: (~product(X,Y,Xy)|~product(Y,Z,Yz)))|~defined(Xy,Z)))|defined(X,Yz))),
% 0.21/10.97 inference(miniscoping,[status(thm)],[f4])).
% 0.21/10.97 fof(f30,plain,(
% 0.21/10.97 ![X0,X1,X2,X3,X4]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~defined(X2,X3)|defined(X0,X4))),
% 0.21/10.97 inference(cnf_transformation,[status(thm)],[f29])).
% 0.21/10.97 fof(f31,plain,(
% 0.21/10.97 ![X,Xyz,Yz]: ((![Y,Z]: ((![Xy]: (~product(X,Y,Xy)|~product(Xy,Z,Xyz)))|~product(Y,Z,Yz)))|product(X,Yz,Xyz))),
% 0.21/10.97 inference(miniscoping,[status(thm)],[f5])).
% 0.21/10.97 fof(f32,plain,(
% 0.21/10.97 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X2,X3,X4)|~product(X1,X3,X5)|product(X0,X5,X4))),
% 0.21/10.97 inference(cnf_transformation,[status(thm)],[f31])).
% 0.21/10.97 fof(f33,plain,(
% 0.21/10.97 ![Y,X]: ((![Yz]: ((![Z]: ~product(Y,Z,Yz))|~defined(X,Yz)))|defined(X,Y))),
% 0.21/10.97 inference(miniscoping,[status(thm)],[f6])).
% 0.21/10.97 fof(f34,plain,(
% 0.21/10.97 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~defined(X3,X2)|defined(X3,X0))),
% 0.21/10.97 inference(cnf_transformation,[status(thm)],[f33])).
% 0.21/10.97 fof(f35,plain,(
% 0.21/10.97 ![Z,Xy]: ((![Yz,X]: ((![Y]: (~product(Y,Z,Yz)|~product(X,Y,Xy)))|~defined(X,Yz)))|defined(Xy,Z))),
% 0.21/10.97 inference(miniscoping,[status(thm)],[f7])).
% 0.21/10.97 fof(f36,plain,(
% 0.21/10.97 ![X0,X1,X2,X3,X4]: (~product(X0,X1,X2)|~product(X3,X0,X4)|~defined(X3,X2)|defined(X4,X1))),
% 0.21/10.97 inference(cnf_transformation,[status(thm)],[f35])).
% 0.21/10.97 fof(f39,plain,(
% 0.21/10.97 ![X,Z]: ((![Y]: ((~defined(X,Y)|~defined(Y,Z))|~identity_map(Y)))|defined(X,Z))),
% 0.21/10.97 inference(miniscoping,[status(thm)],[f9])).
% 0.21/10.97 fof(f40,plain,(
% 0.21/10.97 ![X0,X1,X2]: (~defined(X0,X1)|~defined(X1,X2)|~identity_map(X1)|defined(X0,X2))),
% 0.21/10.97 inference(cnf_transformation,[status(thm)],[f39])).
% 0.21/10.97 fof(f42,plain,(
% 0.21/10.97 ![X0]: (identity_map(codomain(X0)))),
% 0.21/10.97 inference(cnf_transformation,[status(thm)],[f11])).
% 0.21/10.97 fof(f46,plain,(
% 0.21/10.97 ![X0]: (product(codomain(X0),X0,X0))),
% 0.21/10.97 inference(cnf_transformation,[status(thm)],[f15])).
% 0.21/10.97 fof(f49,plain,(
% 0.21/10.97 ![Z,W]: ((![X,Y]: (~product(X,Y,Z)|~product(X,Y,W)))|Z=W)),
% 0.21/10.97 inference(miniscoping,[status(thm)],[f18])).
% 0.21/10.97 fof(f50,plain,(
% 0.21/10.97 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 0.21/10.97 inference(cnf_transformation,[status(thm)],[f49])).
% 0.21/10.97 fof(f51,plain,(
% 0.21/10.97 product(a,b,c)),
% 0.21/10.97 inference(cnf_transformation,[status(thm)],[f19])).
% 0.21/10.97 fof(f52,plain,(
% 0.21/10.97 ![X1,X3]: ((![X2]: (~product(c,X1,X2)|~product(c,X3,X2)))|X1=X3)),
% 0.21/10.97 inference(miniscoping,[status(thm)],[f20])).
% 0.21/10.97 fof(f53,plain,(
% 0.21/10.97 ![X0,X1,X2]: (~product(c,X0,X1)|~product(c,X2,X1)|X0=X2)),
% 0.21/10.97 inference(cnf_transformation,[status(thm)],[f52])).
% 0.21/10.97 fof(f54,plain,(
% 0.21/10.97 product(b,h,d)),
% 0.21/10.97 inference(cnf_transformation,[status(thm)],[f21])).
% 0.21/10.97 fof(f55,plain,(
% 0.21/10.97 product(b,g,d)),
% 0.21/10.97 inference(cnf_transformation,[status(thm)],[f22])).
% 0.21/10.97 fof(f56,plain,(
% 0.21/10.97 ~h=g),
% 0.21/10.97 inference(cnf_transformation,[status(thm)],[f23])).
% 0.21/10.97 fof(f65,plain,(
% 0.21/10.97 defined(a,b)),
% 0.21/10.97 inference(resolution,[status(thm)],[f51,f26])).
% 0.21/10.97 fof(f73,plain,(
% 0.21/10.97 ![X0,X1,X2]: (~product(X0,X1,X2)|~defined(X0,X1)|defined(codomain(X0),X2))),
% 0.21/10.97 inference(resolution,[status(thm)],[f30,f46])).
% 0.21/10.97 fof(f77,plain,(
% 0.21/10.97 ![X0,X1,X2]: (~product(X0,X1,X2)|defined(codomain(X0),X2))),
% 0.21/10.97 inference(forward_subsumption_resolution,[status(thm)],[f73,f26])).
% 0.21/10.97 fof(f78,plain,(
% 0.21/10.97 ![X0,X1,X2]: (~product(c,X0,X1)|~product(b,X0,X2)|product(a,X2,X1))),
% 0.21/10.97 inference(resolution,[status(thm)],[f32,f51])).
% 0.21/10.97 fof(f115,plain,(
% 0.21/10.97 ![X0,X1]: (~defined(X0,X1)|defined(X0,codomain(X1)))),
% 0.21/10.97 inference(resolution,[status(thm)],[f34,f46])).
% 0.21/10.97 fof(f124,plain,(
% 0.21/10.97 ![X0,X1]: (~product(X0,b,X1)|~defined(X0,d)|defined(X1,g))),
% 0.21/10.97 inference(resolution,[status(thm)],[f36,f55])).
% 0.21/10.97 fof(f126,plain,(
% 0.21/10.97 ![X0,X1]: (~product(X0,b,X1)|~defined(X0,d)|defined(X1,h))),
% 0.21/10.97 inference(resolution,[status(thm)],[f36,f54])).
% 0.21/10.97 fof(f258,plain,(
% 0.21/10.97 ~defined(a,d)|defined(c,g)),
% 0.21/10.97 inference(resolution,[status(thm)],[f124,f51])).
% 0.21/10.97 fof(f294,plain,(
% 0.21/10.97 ~defined(a,d)|defined(c,h)),
% 0.21/10.97 inference(resolution,[status(thm)],[f126,f51])).
% 0.21/10.97 fof(f323,plain,(
% 0.21/10.97 defined(a,codomain(b))),
% 0.21/10.97 inference(resolution,[status(thm)],[f115,f65])).
% 0.21/10.97 fof(f334,plain,(
% 0.21/10.97 ![X0]: (~defined(codomain(b),X0)|~identity_map(codomain(b))|defined(a,X0))),
% 0.21/10.97 inference(resolution,[status(thm)],[f323,f40])).
% 0.21/10.97 fof(f338,plain,(
% 0.21/10.97 ![X0]: (~defined(codomain(b),X0)|defined(a,X0))),
% 0.21/10.97 inference(forward_subsumption_resolution,[status(thm)],[f334,f42])).
% 0.21/10.97 fof(f492,plain,(
% 0.21/10.97 defined(codomain(b),d)),
% 0.21/10.97 inference(resolution,[status(thm)],[f77,f55])).
% 0.21/10.97 fof(f2851,plain,(
% 0.21/10.97 defined(a,d)),
% 0.21/10.97 inference(resolution,[status(thm)],[f338,f492])).
% 0.21/10.97 fof(f2862,plain,(
% 0.21/10.97 defined(c,h)),
% 0.21/10.97 inference(backward_subsumption_resolution,[status(thm)],[f294,f2851])).
% 0.21/10.97 fof(f2863,plain,(
% 0.21/10.97 defined(c,g)),
% 0.21/10.97 inference(backward_subsumption_resolution,[status(thm)],[f258,f2851])).
% 0.21/10.97 fof(f2872,plain,(
% 0.21/10.97 product(a,d,compose(a,d))),
% 0.21/10.97 inference(resolution,[status(thm)],[f2851,f24])).
% 0.21/10.97 fof(f2882,plain,(
% 0.21/10.97 product(c,h,compose(c,h))),
% 0.21/10.97 inference(resolution,[status(thm)],[f2862,f24])).
% 0.21/10.97 fof(f2905,plain,(
% 0.21/10.97 product(c,g,compose(c,g))),
% 0.21/10.97 inference(resolution,[status(thm)],[f2863,f24])).
% 0.21/10.97 fof(f4435,plain,(
% 0.21/10.97 ![X0]: (~product(b,h,X0)|product(a,X0,compose(c,h)))),
% 0.21/10.97 inference(resolution,[status(thm)],[f2882,f78])).
% 0.21/10.97 fof(f4436,plain,(
% 0.21/10.97 ![X0]: (~product(c,X0,compose(c,h))|h=X0)),
% 0.21/10.97 inference(resolution,[status(thm)],[f2882,f53])).
% 0.21/10.97 fof(f4502,plain,(
% 0.21/10.97 ![X0]: (~product(b,g,X0)|product(a,X0,compose(c,g)))),
% 0.21/10.97 inference(resolution,[status(thm)],[f2905,f78])).
% 0.21/10.97 fof(f5442,plain,(
% 0.21/10.97 ![X0]: (~product(a,d,X0)|compose(a,d)=X0)),
% 0.21/10.97 inference(resolution,[status(thm)],[f2872,f50])).
% 0.21/10.97 fof(f11109,plain,(
% 0.21/10.97 product(a,d,compose(c,h))),
% 0.21/10.97 inference(resolution,[status(thm)],[f4435,f54])).
% 0.21/10.97 fof(f11110,plain,(
% 0.21/10.97 compose(a,d)=compose(c,h)),
% 0.21/10.97 inference(resolution,[status(thm)],[f11109,f5442])).
% 0.21/10.97 fof(f11152,plain,(
% 0.21/10.97 ![X0]: (~product(c,X0,compose(a,d))|h=X0)),
% 0.21/10.97 inference(backward_demodulation,[status(thm)],[f11110,f4436])).
% 0.21/10.98 fof(f11322,plain,(
% 0.21/10.98 product(a,d,compose(c,g))),
% 0.21/10.98 inference(resolution,[status(thm)],[f4502,f55])).
% 0.21/10.98 fof(f11323,plain,(
% 0.21/10.98 compose(a,d)=compose(c,g)),
% 0.21/10.98 inference(resolution,[status(thm)],[f11322,f5442])).
% 0.21/10.98 fof(f11371,plain,(
% 0.21/10.98 product(c,g,compose(a,d))),
% 0.21/10.98 inference(backward_demodulation,[status(thm)],[f11323,f2905])).
% 0.21/10.98 fof(f11372,plain,(
% 0.21/10.98 h=g),
% 0.21/10.98 inference(resolution,[status(thm)],[f11371,f11152])).
% 0.21/10.98 fof(f11394,plain,(
% 0.21/10.98 $false),
% 0.21/10.98 inference(forward_subsumption_resolution,[status(thm)],[f11372,f56])).
% 0.21/10.98 % SZS output end CNFRefutation for theBenchmark.p
% 0.21/10.99 % Elapsed time: 0.542621 seconds
% 0.21/10.99 % CPU time: 4.137536 seconds
% 0.21/10.99 % Total memory used: 78.533 MB
% 0.21/10.99 % Net memory used: 71.788 MB
%------------------------------------------------------------------------------